# Communication in Mathematical Modeling and Applications

Publications
This paper presents minimal construction techniques of a new graph class called Ferrer-esque [10] comes from Ferrers relation [9] on path and cycle graphs by using set cover method. The minimal constructions provide to obtain a Ferrer-esque graph by adding minimum number of edges to paths and cycles. We also state some open problems about Ferrer-Esque graphs to the readers.

We take the results of existence and uniqueness of the solution for doubly reflected backward stochastic differential equations (BSDEs in short) proved recently by Hassairi in [7], we study its connection with Dynkin games problem under very weak assumptions. We show in the present paper that this differential game have a value function and a saddle point.

There are quite complicated rules and constraints that can be imposed by the bank when the loan issued. Bank branches, which play a direct role in the credit, must accurately determine the customer's credit request to eliminate these difficulties and create an effective payment system according to the customer. In the study, 100 random loan applications made in 2016 of a bank branch operating in the Black Sea Region were examined. These customer demands are affecting customer characteristics. The "Logistic Regression (LR) Model" was created to predict creditworthiness according to the identified fugitives. In the model, customer age, education, marital status, debt grade, credit card debt, other debts, cross product are the variables. These are statistically significant in terms of marital status, gender, cross product, or creditworthiness. However, various variables such as debt income ratio, credit card debt, and other debts are statistically significant and affect credibility to negatively. In addition, occupational, income and educational constraints were found to be meaningless. With this model, the factors affecting the credit were evaluated. As a result of the study, the bank branch will benefit from the statistical model in which it is created, to evaluate according to the customer characteristics in its portfolio, and to give more credit to branch customers.

In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with cubic trigonometric B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L 2 , L ∞ are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result of the proposed method with the exact solution to show the convergence and advantages of the new method. The results got by present wavelet method are compared with that of by collocation method based on radial basis functions method. Finally, the numerical examples explain the accuracy of this method.

In this study, we first show that the system of Frenet-like differential equation characterizing timelike curves of constant breadth is equivalent to a third order, linear, differential equation with variable coefficients. Then, by using a rational approximation based on Bernstein polynomials, we obtain the set of solution of the mentioned differential equation under the given initial conditions. Furthermore, we discuss that the obtained results are useable to determine timelike curves of constant breadth in Minkowski 3-space E 3 1 .

Two Darboux transformations of the Korteweg-de Vries (KdV) equation and Boussinesq equation are constructed through the Darboux method. Soliton solutions of these two equations are presented by applying the Darboux transformations.

This study introduces a new bowling scoring system and testsits consistency with the current scoring system with respectto preserving player placements. A comprehensive simulation study for different scenarios; two-player, three-player, and four-playergames performed. The simulations empirically quantify thelikelihood of experiencing concordant results between thetwo (currentand new) systems. The simulation study revealed that the percentage of times that the current and new scoring systems yield the sameplacements at least 85% when two players compete, at least 66% of the time when three players compete, and at least 43% of the timewhen four players compete regardless of the ability levels of the players. A comparison study using real bowling data-sets have beendone and showed the consistence for the new scoring system with the current one. However, the new scoring system is easy tocalculate,understand and to be implemented. Keywords: Scoring System, bowling, conditional modeling, categorical data analysis, cumulative logit model

In this paper, the parallel ruled surfaces with Darboux frame are introduced in Euclidean 3-space. Then some characteristic properties such as developability, striction point and distribution parameter of the parallel ruled surfaces with Darboux frame are given in Euclidean 3-space. Then we obtain Steiner rotation vector of this kind of surfaces Euclidean 3-space. By using this rotation vector, we compute pitch length and pitch angle of the parallel ruled surfaces with Darboux frame.

Chebyshev wavelets operational matrices play an important role for the numeric solution of rth order differential equations. In this study, operational matrices of rth integration of Chebyshev wavelets are presented and a general procedure of these matrices is correspondingly given. Disadvantages of Chebyshev wavelets methods is eliminated for rth integration of Ψ (t). The proposed method is based on the approximation by the truncated Chebyshev wavelet series. Algebraic equation system has been obtained by using the Chebyshev collocation points and solved. The proposed method has been applied to the three nonlinear boundary value problems using quasilinearization technique. Numerical examples showed the applicability and accuracy.

The purpose of this study is to apply the Chebyshev collocation method to the two-dimensional heat equation. The method converts the two-dimensional heat equation to a matrix equation, which corresponds to a system of linear algebraic equations. Error analysis and illustrative example is included to demonstrate the validity and applicability of the technique.

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the neutral functional-differential equations (NFDEs) with proportional delays. By using Hermite polynomials and collocation points, NFDEs and the given conditions are transformed into matrix equation which corresponds to a system of linear algebraic equations with unknown Hermite coefficients. Hence, by solving this system, the unknown Hermite coefficients are computed. In addition, some numerical examples are given and comparisons with other methods are made in order to demonstrate the validity and applicability of the proposed method.

In this paper, heat transfer study of porous fin with temperature-dependent thermal conductivity and internal heat generation is analyzed numerically using Legendre wavelet collocation method. The numerical solutions are used effects of nonlinear thermal conductivity, convective and porosity parameters on the thermal conductivity of the fin. The Legendre wavelet collocation method is verified with the results of numerical method using Runge-Kutta method and good agreements are established.

In 1999, Molodtsov introduced soft set theory which is a new mathematical tool for dealing with uncertainties and is free from the difficulties affecting the existing methods. Research works on soft set theory are progressing rapidly. Combining soft sets with fuzzy sets and intuitionistic fuzzy sets, Maji et al. , defined fuzzy soft sets and intuitionistic fuzzy soft sets which are rich potentials for solving decision making problems. It has been found that soft set, fuzzy set and rough set are closely related concepts. In this work, we define intuitionistic fuzzy soft set aggregative operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.

The stability analysis of infectious disease model in a dynamic population is studied.The recruitment rate into the susceptible population is introduced since the population is dynamic thereby allowing a varying pouplation as a result of migration and birth.The model exhibited two equilibria: the disease free and endemic. The local stability of the model is asymptotically stable when R 0 < 1 and unstable when R 0 > 1. The global stability analysis of the disease free shows that the system is globally stable when the first derivative of Lyapunov function is negative.

This study aimed at making an investigation on entropy generation in unsteady MHD generalized couette flow with convective cooling. Specifically the study intended to; develop flow model for a case of nanofluid in a channel, determine the effect of different parameters on velocity, temperature and entropy generation and to determine the effect of magnetic field on the flow on an entropy generation. Also the study aim to come up with distinctively recommendation on dynamics of entropy generation, temperature variation and velocity profiles in unsteady MHD flow with convective cooling. Findings showed that an increase in nanoparticles and Reynolds number leads to increase in the velocity while pressure gradient, MHD and nanofluid fraction held constant. It is evidently that Alumina-water nanofluid tends to raise the velocity profile faster than Copper-water nanofluid. Also the results show that an increase in Eckert number causes the decrease in temperature profile. Further, it was noticed that Copper-water nanofluid tends to raise the temperature profile faster than Alumina-water nanofluid. More interestingly it was observed that the entropy generation rises as the result of increase in Eckert number. Also it is noticed that entropy generation rises in lower plate but when it comes closer the upper plate the entropy generation rate starts to fall as the result of increase in nanoparticles.

In this paper, firstly, new Hermite-Hadamard-Fejer type inequalities for p-convex functions in fractional integral forms are built. Secondly, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for p-convex functions in fractional integral forms are obtained. Finally, some Hermite-Hadamard and Hermite-Hadamard-Fejer inequalities for convex, harmonically convex and p-convex functions are given. Many results presented here for p-convex functions provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

In this paper, we study a certain class of equations that model the propagating in dual-core fibers. Linear stability analysis is applied to discuss the existence of some types of travelling wave solutions and to compute the wave speed. New doubly periodic solutions are obtained, and new bright and dark soliton solutions are found.

In this paper, we present general fractional representation formulae for a function in terms of the fractional Riemann-Liouville integrals of different orders of the function and its ordinary derivatives. We also use these Montgomery identities to establish some new Ostrowski type integral inequalities.

Communication is supposed to be continuous in a network design. It is important for a network to be tough so that communication is not interrupted in case any damage. In this paper, it is investigated how to decide which graph model to choose, when a selection is needed to make between different graphs to be used for a network model when all known vulnerability measures are same. We introduce the concept of the average weakly edge domination number of a graph as a new vulnerability measure. We establish relationships between the average weakly edge domination number and some other graph parameters, and the extreme values of given measure among all graphs and average weakly edge domination number for some families of graphs. Also a polynomial time algorithm with complexity O(n^3) is given.

Predator-prey model is useful and often used in the environmental science field because they allow researchers both to observe the dynamic of animal populations and make predictions as to how they will develop over time. One of the most ecological applications of differential equations system is predator prey problem. In this paper, we will discuss about shark and fish Lotka-Volterra modified predator prey model in differential equation. The solution, existence, uniqueness and boundedness of the solution of the model are investigated. We also analyze about the steady state and stability criteria using Jacobian matrix method. Finally, numerical simulations are carried out to justify analytical results.

In this paper, non-polynomial spline method for solving the generalized regularized long wave (GRLW) equation are presented. In this paper, we take deferent spline functions. The stability analysis using Von-Neumann technique shows the scheme is marginally stable. To test accuracy the error normsL 2 , L ∞ are computed. Also, the change in conservation quantities are evaluated which are found to be very small. To illustrate the applicability and efficiency of the basis, we compare obtained numerical results with other existing recent methods. Moreover, interaction two and three solitary waves are shown. The development of the Maxwellian initial condition into solitary waves is also shown and we show that the number of solitons which are generated from the Maxwellian initial condition can be determined.

Top-cited authors
• Al-Azhar University
• Kırklareli University
• Kirklareli University
• Eskisehir Osmangazi University
• Menoufia University